Rolling method for rolling mills

ABSTRACT

A rolling method for rolling mills wherein, in determining a rolling schedule for the rolling mills, a mean rolling reduction and the number of passes in which the desired total rolling reduction is achieved in a minimum period of time are obtained from the rolling specifications including the hardness of rolled material, the allowable maximum load, the allowable maximum torque and the limit of the biting angle, and the detected values of the temperature and thickness of parent material at the entrance side of the rolling mill. In carrying the schedule into practice, a value smaller than the mean rolling reduction is selected as a rolling reduction for each pass in initial and terminating stages of the rolling operation, while a value larger than the mean rolling reduction is selected as a rolling reduction for each pass in other stages, whereby the sum of the rolling reductions obtained in all the passes can be made equal to the product of the mean rolling reduction and the number of passes.

United States Patent Morooka ROLLING METHOD FOR ROLLING MILLS [75] Inventor: Yasuo Morooka, Hitachi, Japan Primary Examiner-Milton S. Mehr Attorney, Agent, or Firm-Craig & Antonelli [57] ABSTRACT [73]: Asslgnee' Japan A rolling method for rolling mills wherein, in determining a rolling schedule for the rolling mills, a mean [22] 1975 rolling reduction and the number of passes in which the desired total rollin reduction is achieved in a min- 21 g l 1 App] No 568l93 unum period of time are obtained from the rollmg specifications including the hardness of rolled material, the allowable maximum load, the allowable maxi- [30] F0 8 Apphcafion Pnonty Dam mum torque and the limit of the biting angle, and the Apr. l7, I974 Japan 49-42l48 d t t d valu s of the temperature and thickness Of parent material at the entrance side of the rolling mill. 52 us. c1 72/6; 72/13 In carrying the Schedule q p q a value smaller 51 Int. c1. B21B 37/00 the mean rolllng reductlon 18 selected as a rolhng [58] Field 01 Search 72/6, 8, 16, 13, 19 reduction P in initial and terminating stages of the rolling operation, while a value larger 5 References Cited than the mean rolling reduction is selected as a rolling UNITED STATES PATENTS reduction for each pass in other stages, whereby the sum of the rolling reductions obtained in all the passes 3 can made equal to the product of the mean rolling 3:600:9l9 8/l97l sindzingrezz 1111111111.. 1218 and umber Passes 3,688,555 9/1972 Minami et al 72/8 12 Claims, 6 Drawing Figures 1 1 3 scREw-oom POSITlCN SETTING .MQL l F 2 1 FIRST secouo THIRD G ATE ARITHMETD ARITHMETC MARITHMETIC UNIT UNIT Ahl UN" 51 CIRCUIT c 7 8' IO R, a I TX M G 4 Fur or TEMP. or nous: mm DETECTED worrumozsswmummrsmu.

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WW RQJ. DIAIETE? lNPUTW LMT LOAD l cucuumu (F IEPN DEFWATION RESlSTPNCE OF ROLLED MEIERW.

PAS

or TOTAL no, OF

(EQUATION r61 US. Patent Dec. 23, 1975 Sheet 1 of3 3,927,545

ROLLING REDUCTION LIMIT ToTAL ROLLING TIME ROLLING REDUCTION (Ah) Ahmclx FIG. 2

THICKNESS TEMPERATURE OF ROLLED MATERIAL NUMBER OF PASSES US. Patent Dec. 23, 1975 Sheet 2 of3 Fl G. 3 I I 3 SCREW-DOWNI 4 POSITION I SETTING I I MEANS 6 I I L L FIRST SECOND THIRD GATE ARITHMETIC ARITHMETIO ARITHMETIC CIRCUIT UNIT Ah UNIT Ahl UNIT L T 8 IO .Px.Zx.Ahx FIG. 4

INPUT OF TEMP. OF ROLLED MATERIAL DETECTED INPUT OF THICKNESS OF ROLLED MArERIAL VAUJES I INPUT OF HARDNESS 0F ROLLED MATERIAL INPUT 0F DESIRED ROLLING REDUcTION SET VALUES INPUT OF ROLL DIAMETER INPUT OF LIMIT LOAD INPUT OF LIMIT ROLLING TORQUE INPUT OF LIMIT ROLLING REDUCTION CALCULATION OF LIMITED ROLLING REDUCTION IFORMULAS I2 TO|5I D'EAI'SEISREIISIMTION OF TOTAL NO. OF IEQUATION I6) DETERMINATION OF MEAN ROLLING REDUCTION (EQUATION I7) US. Patent Dec. 23, 1975 Sheet3of3 3,927,545

FIG.

THICKNES ROLLING METHOD FOR ROLLING MILLS BACKGROUND OF THE INVENTION This invention relates to rolling methods for rolling mills, and more particularly it deals with a rolling method for rolling mills which is suitable for carrying out rolling in a minimum period of time, and effecting temperature control and contour control.

Several proposals have been made regarding rolling methods for rolling mills. They include, for example, a method described in Japanese Patent Publication No. 27042/7l entitled Optimum Rolling Method for Hot Rolling Mills of the Reversible Type". In this method, the rolling torque for each pass is assumed to be of the same value. and the maximum allowable rolling torque for effecting rolling in a minimum period of time is obtained by utilizing the fact that the relation between the rolling torque and the total rolling time is as shown in FIG. 1 of the Publication, with the number of passes being taken as a parameter. Then the value of a rolling reduction for each pass is determined based on the maximum allowable rolling torque.

The aforementioned and other rolling methods that have hitherto been proposed only aim at carrying out rolling in a minimum period of time, and they are basi cally based on the concept of increasing as much as possible to value of a rolling reduction for each pass. Accordingly, when these methods are employed for effecting rolling, reduction in the thickness of the rolled material can be achieved quickly. However, as the thickness of the rolled material is reudced, the rolled material shows a rapid drop in temperature, thereby making it impossible to maintain at the desired value the temperature of the rolled material when the rolling operation is completed. As is well known, the rolled material is air cooled according to the Stefan- Boltzmann law. More specifically, the reduction in temperature due to air cooling is proportional to the entire surface area of the rolled material, so that if the value of a rolling reduction for each pass in initial stages of the rolling operation is high, then the rolled material will show a great reduction in temperature in passing it in initial stages of the operation and its temperature will become too low when it is passed in terminating stages of the operation. As a result, the temperature of the rolled material will be below the predetermined level when the rolling operation is completed.

Moreover, too great a reduction in the temperature of the rolled material in terminating stages of the operation would make it necessary to apply to the rolling stand a rolling load which is above the predetermined level, in order to achieve the desired total rolling reduction. This would make it impossible to produce products of good contour. That is, an increase in the rolling load would increase the degree of bending of the rolls, thereby making it impossible to impart a good crown to the rolled material. Also, load which is too high would cause the surface ofthe rolled material to lose luster. In order to induce the rolled material to take a good crown, rolling mills in use nowadays are provided with a roll bending device for correcting a crown imparted to the rolls. It is to be noted that this device operates satisfactorily when the rolling load is below a range between 700 to 800 tons. It will thus be seen that it is essential that the temperature of the rolled material be in the neighborhood of a suitable value when it is 2 passed in terminating stages in order satisfactorily to effect contour control of the rolled products.

SUMMARY OF THE INVENTION A principal object of the present invention is to provide a rolling method for rolling mills which enables to produce rolled products of high quality in a stable manner by obviating the afore-mentioned problems raised in effecting temperature control and contour control in rolling methods of the prior art.

Another object of the invention is to provide a rolling method for rolling mills wherein no high loads are ap plied to the rolling mill and the screwdown electric motor.

Another object of the invention is to provide a rolling method for rolling mills which enables to satisfactorily effect temperature control and contour control in a simple and practical manner.

The outstanding characteristics of the invention are that at first a mean rolling reduction Ah and the number n of passes in which the desired total rolling reduction is achieved in a minimum period of time are ob tained from the rolling specifications including the hardness of rolled material, the allowable maximum rolling load, the allowable maximum rolling torque, the limit of the biting angle, the desired thickness of sheet material at the exit side of the rolling mill and the desired temperature at the exit side of the rolling mill, and the detected values of the thickness and temperature of sheet material at the exit side of the rolling mill, and then the rolling schedule is determined such that pass ing is effected in initial and terminating stages of the operation with a rolling reduction of a value lower than the mean rolling reduction Ah and yet the total rolling reduction achieved is equal to the product of the mean rolling reduction Ah and the number n of passes in which the desired total rolling reduction is achieved.

One of the features of the invention is that, in calculating a mean rolling reduction, a maximum limit rolling reduction, a load rolling reduction and a torque limited rolling reduction are obtained and the smallest value of these rolling reductions is used.

Another feature of the invention is that, in calculating the number of passes, the ratio of the desired total rolling reduction to a value obtained by multiplying the smallest value of the rolling reductions by a coefficient smaller than one, is obtained and the value obtained is used as the number of passes by counting the fraction of the value as a whole number.

Another feature of the invention is that, in calculating the number of passes, the ratio of the desired total rolling reduction to a value obtained by multiplying one of the maximum limit rolling reduction, the load limited rolling reduction and the torque limited rolling reduction by a coefficient smaller than one is obtained and the value obtained is used as the number of passes by counting the fraction of the value obtained as a whole number.

Another feature of the invention is that, in calculating the number of passes, the ratio of the desired total rolling reduction to a value obtained by multiplying the mean value of the maximum limit rolling reduction, the load limited rolling reduction and the torque limited rolling reduction by a coefficient smaller than one is obtained and the value obtained is used as the number of passes by counting the fraction of the value obtained as a whole number.

Another feature of the invention is to calculate the load limited rolling reduction by using the detected values of the temperature and thickness of material to be rolled.

Another feature of the invention is to calculate the torque limited rolling reduction by using the detected values of the temperature and thickness of material to be rolled.

Another feature of the invention is to obtain a rolling reduction for each pass in initial and terminating stages of the rolling operation as the product of the mean rolling reduction and a distribution rate.

Another feature of the invention is to obtain the distribution rate as a function of the number of passes.

Another feature of the invention is to obtain a rolling reduction for each pass in initial and terminating stages of the rolling operation from the cumulative distribution ratio of the thickness of parent material to that of the product.

Another feature of the invention is to obtain the cumulative distribution ratio as a function of the number of passes.

BRIEF DESCRIPTION OF THE DRAWINGS FIG. 1 is a diagrammatic representation of the rolling reductions in relation to the total rolling time;

FIG. 2 is a diagrammatic representation of the thickness in relation to the temperature of material to be rolled with the number of passes being used as a parameter;

FIG. 3 is a systematic view showing one embodiment of the invention;

FIG. 4 is a chart showing the order in which the mean rolling reduction and the number of passes in which the desired total rolling reduction is achieved are calculated;

FIG. 5 is a diagrammatic representation of the relation between the cumulative load distribution ratio, the number of passes and the thickness, the cumulative load distribution ratio being used in a calculating method of a rolling reduction for each pass from the mean rolling reduction; and

FIG. 6 is a diagrammatic representation of the relation between the distribution ratio and the number of passes, the distribution ratio being used in an other calculating method of a rolling reduction for each pass from the mean rolling reduction.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT The present invention will now be described in detail by using equations and referring to the accompanying drawings. The principle of the invention will first be described.

The rolling time t, for each pass can be expressed by the following equation:

where I is the length of rolled material at the exit side of the rolling mill for each pass, and v; is the mean rolling velocity.

The length I of the rolled material can be expressed by the following equation:

where H is the thickness of the rolled material before rolling, 3,, is the width of the rolled material before rolling, L is the length of the rolled material before rolling, h, is the thickness of the rolled material after rolling in each pass, and b,- is the width of the rolled material after rolling in each pass.

h, and b in equation (2) are related to each other as follows:

i h =H,, 2 Ah] (3) where Ah, is the rolling reduction achieved in each pass, and B is the coefficient of the increase in width. The increase in width may, for all practical purposes, be neglected and dropped from the equation. That is B 0. Thus, in the following description, the increase in width is neglected in the interest of brevity. Accordingly, the time t required for each passing can be expressed as follows from the foregoing relations:

H, 2 Ah,

If the rolling reduction Ah, for each pass is averaged to obtain a mean rolling reduction Ah, equation (5) can be further converted into the following equation (6):

I; From equation (6), the time T required for effecting the desired total rolling reduction in all the passes can be expressed by the following equation, wherein the rolling velocity is constant for all the passes or v, v.

As can be seen clearly in equation (7), the total rolling time T is a function of the mean rolling reduction Ah with the number n of passes being a parameter. FIG. 1 shows the reduction between the mean rolling reduction and the total rolling time by combining conditional equation (8) with equation (7). As can be seen clearly in FIG. 1, the smaller the number of passes, the shorter is the total rolling time, and the smaller the mean rolling reduction Ah, the shorter is the total rolling time, provided that the number of passes remains unaltered. If it is desired to reduce the number of passes, one has only to increase the mean rolling reduction Ah. However, it is impossible to indefinitely increase the rolling reduction, and the rolling reduction must be below a rolling reduction limiting value Ah max which may vary depending on limitations placed on the biting angle, limitations placed on the rolling load and limitations placed on the rolling torque. It is when the rolling reduction in each pass is uniform and its value is equal to the rolling reduction limiting value Ah max that the rolling reduction in any pass does not exceed the rolling reduction limit value Ah max and yet the mean rolling reduction can be maximized. Thus, the number of passes is n as shown in FIG. 1 when the total rolling time is minimized, and it is at A point in FIG. 1 that the total rolling time is minimized. it will be evident from equation (7) that the A point satisfies the following relation:

From the foregoing, it will be appreciated that the essential minimum condition for realizing the shortest rolling time is that the rolling reduction for each pass should be uniform and its value should be below the rolling reduction limiting value Ah max, and that the number of passes should be minimized. The value of the minimum number of passes can be obtained by substituting into equation (10) the rolling reduction limiting value Ah max as a mean rolling reduction Ah. Since n must be an integer when it is obtained from equation (10), the value of n obtained may be made into in integer by counting the fraction as a whole number. 1f the value of n obtained in this way is used in equation (9), then it is possible to obtain the value of the mean rolling reduction Ah which corresponds to the A point in FIG. I.

It should be noted, however, that when rolling is carried out by using the mean rolling reduction Ah and the number n of passes obtained as aforesaid and by using the same value as the rolling reduction for each pass, it will be impossible to effect temperature control and contour control as aforementioned. The temperature of rolled material shows variations with time, with the values of the temperature varying depending on the rolling reduction as shown in FIG. 2. A curve I represents a rolling process in which the rolling reduction is uniform for all the passes. when this process is used, it will be seen that the amount of heat retained in the rolled product is high in passes in terminating stages of the operation, and that the temperature of the rolled product is high at the time the final passing is completed. On the other hand, a curve [I represents a rolling process in which the rolling reduction which is high in initial stages of operation is gradually lowered. The use of this rolling process gives a small amount of heat retained in the rolled material when the final pass is reached, so that the temperature of the rolled product is low upon completion of the final passing. From this observation, it will be appreciated that, if it is desired to control the temperature of rolled material by adjusting rolling reductions, one has only to reduce the rolling reduction for each pass in initial stages of the operation and increase the rolling reduction for each pass in intermediate and terminating stages of the operation.

Rolling reductions in terminating stages are an important factor in effecting contour control. Control of widthwise or edge-to-edge thickness of rolled material to produce uniform flatness is effected by controlling the bending of the rolls in passes in initial stages of operation. However, since the bending of the rolls may vary in proportion to the rolling load, rolling reductions are affected by this factor. For example, it is possible to produce uniform flatness or good contour if rolling reductions are such that the rolling load is about 700 tons. From this, it will be appreciated that contour control makes it necessary to reduce rolling reductions for passes in terminating stages of the operation.

As aforementioned, if it is desired to obtain a.minimum rolling time with effecting temperature control and contour control at the same time, it would be necessary to increase a mean rolling reduction as much as is practicable and to vary a rolling reduction for each pass without adopting a uniform value for a rolling reduction for each pass, in such a manner that a rolling reduction smaller in value than the mean rolling reduction Ah is selected for each pass in initial stages of the operation, a rolling reduction greater in value than the mean rolling reduction Ah is selected for each pass in intermediate stages of the operation, and a rolling reduction smaller in value than the mean rolling reduction Ah is selected again for each pass in terminal stages of the operation. Although the rolling reduction for each pass in intermediate stages should be greater in value than the mean rolling reduction Ah, it is important that it should not exceed the rolling reduction limiting value Ah max. Thus, according to the invention, the mean rolling reduction Ah should be slightly smaller in value than the rolling reduction limiting value Ah max.

According to the invention, the number n of passes which would enable to obtain a minimum rolling time is obtained from equation (ID). in performing calculation, a value slightly smaller than the rolling reduction limiting value Ah max or qb. Ah max (0 qb 5 l) is substituted into the equation 10) to obtain the number n of passes. If the calculated value of the number n of passes has a fraction, the fraction should be counted as a whole number so that the value may be an integer. Then the value of the number n of passes obtained in this way is substituted into equation (9) to calculate the mean rolling reduction Ah. Thereafter a rolling reduction for each pass is calculated by correcting the mean rolling reduction Ah for each pass. The correction of the rolling reduction for each pass is effected such that the rolling reductions for passes in initial and terminating stages should become smaller in value than the mean rolling reduction Ah- The method for effecting correction is subsequently to be described. The aforesaid coefficient rl) can be selected beforehand empirically or experimentarily.

A preferred embodiment of the invention will be described with reference to the drawings. FIG. 3 is a systematic view showing the embodiment. In the figure, l is a material to be rolled, 2 a reversible rolling mill, and 3 a screw-down electric motor for positioning the rolling mill for effecting screw-down. 4 is a radiation pyrometer for detecting the initial entrance side temperature of the material 1 to be rolled, and 5 a thickness meter for detecting the initial entrance side thickness of the material 1. 6 refers to a first arithmetic unit for calculating the total number n of passes and an average rolling reduction Ah which would enable the desired total rolling reduction to be achieved in a minimum interval of time. 7 refers to a second arithmetic unit for calculating a rolling reduction Ah, for each pass by taking temperature control and contour control into consideration. 8 refers to a third arithmetic unit for determining a screw-down position at which the rolling mill should be set based on the rolling reduction Ah,- for each pass calculated by the second arithmetic unit 7, 9 designates a load cell which detects whether or not the material I is bitten by the rolls to time nicely the setting of the screw-down position of the rolls for each pass. 10 designates a gate circuit which switches to the rolling mill an output of the third arithmetic unit 8 when signal from the load cell 9 indicates that the material I is not bitten by the rolls. ll refers to a screw-down position setting means for setting the rolling mill at a screwdown position indicated by an output of the gate circuit l0.

in the system of the aforementioned construction, the first arithmetic unit 6 is rendered operative to perform calculation when the material 1 to be rolled is withdrawn from a soaking pit (not shown) or the like and reaches the pyrometer 4 and thickness meter 5. From outputs of the pyrometer 4 and thickness meter 5, the first arithmetic unit 6 calculates the total number of passes and a mean rolling reduction adapted to achieve the desired total rolling reduction in a shortest interval of time, and the result of calculation is produced as an output. The process of calculation performed by the first arithmetic unit 6 will be described with reference to FIG. 4.

First of all, a temperature To and a thickness H,, of the material 1 before rolling reductions are fed into the unit 6. Then information .Q on the hardness of the material 1 to be rolled, eg the carbon content of the material, and a final thickness h, to be produced in the rolled product are fed into the unit 6 as set values. Also, a maximum limit rolling reduction Ah, which may vary depending on the diameter R of the rolls of the rolling mill, the biting angle limit value 8,. and the types of steel is inputed as a set constant. For example, the maximum limit rolling reduction Ah, may be obtained from the equation;

Ah, 2R (l-cos 9,).1yfl where 190 the constant depending on the type of steel.

Then the diameter R of the rolls, an allowable maximum rolling load P, and an allowable maximum rolling torque r, are fed into the unit 6. From these values as well as the detected temperature T,, and hardness Q of the material 1 to be rolled, maximum limit rolling reductions Ah,, and Ah 1- corresponding to rolling load limit and rolling torque limit are calculated. For performing calculation of Ah, and Ah 1 it is possible to adopt a method whereby the temperature and hardness of the material to be rolled, the limit load, and the limit torque are substituted into the known rolling load equation and rolling torque equation, and the rolling reductions are obtained by calculating in the reverse order. In this embodiment, calculation is carried out as presently to be described.

First of all, a mean value of the initial thickness H of the material 1 detected by the thickness meter 5 and the final thickness hp to be produced in the rolled product is calculated by the formula, 11,, =05. (H, hp). Then a rolling pressure P per unit area is calculated from the mean value h,,,, the initial temperature T the hardness Q, and the maximum limit rolling reduction Ah I by using a known deformation resistance equation and a known rolling load correcting term equation. More specifically, P is calculated as follows:

where a, b, c and d: The coefficients.

(I: The carbon content (percent). T The temperature (K) of the material to be rolled.

The draft percentage.

A: The strain velocity (l/Sec). k,: The deformation resistance.

A minimum value is selected from among the values of Ah, and AM obtained by equations (14) and (I5) and the value of set maximum limit rolling reduction Ah,, and the minimum value thus selected is used as the rolling reduction limiting value Ah max which is multiplied by (0 5 S l) to obtain a limited rolling reduction Ah For example, a value 0.8 may be selected for dz.

From the limited rolling reduction Ah determined as aforementioned, the total number n of passes and the mean rolling reduction Ah are determined by the following formula which utilizes equations and Where the brackets 1 indicates that any fraction is counted as a whole number.

By using the value of n obtained from formula (16), we get The first arithmetic unit feeds as outputs into the second arithmetic unit 7 the total number n of passes and the mean rolling reduction Ah,, obtained finally from equations (16) and (17).

The outputs n and Ah of the first arithmetic unit 6 are inputed to the second arithmetic unit 7 where a rolling reduction Ah, for each pass is determined. The method used for determining the value of rolling reduction Ah will be described with reference to FIG. 5 which shows the relation between the cumulative load distribution ratio q, the number of passes n, and the thickness h This functional relation has been determined empirically from the data obtained by practicing rolling operations, and can be expressed as, the following equations:

where n is the total number of passes, i is a number of each pass, and a, b and c are the coefficients.

In equation, (l8), h, H when e, 0, and h h, when e, I, so that B=A.H,,"" (Zl). As a result, the rolling reduction Ah, for each pass can be calculated from the following formula in view of the equations (18), (20) and (2l):

Thus, in the second arithmetic unit 7, the cumulative distribution ratio 6,- for each pass is obtained by equation (19), and the value of 6; obtained in this way is substituted into equation (22), so that the thickness h, to be produced in each pass can be calculated. Thus the rolling reduction Ah for the first pass can be obtained from the following equation:

Ah =h h ln obtaining the cumulative load distribution value from equation 19) by calculation, care should be taken as specified hereinafter. That is, the coefficients a. b and c in equation 19) should satisfy the following conditions:

1. Limitations are placed on the rolling reduction by taking temperature control into consideration in passes in initial stages;

2. The value of rolling reduction in passes in intermediate stages is below that of the rolling reduction limiting value Ah max; and

3. Limitations are placed on the rolling reduction by taking contour control into consideration in terminating stages.

In this way, the second arithmetic unit 7 calculates the thickness to be produced or rolling reduction to be achieved in each pass and transmits as its outputs the values obtained to the third arithmetic unit 8.

The third arithmetic unit 8 makes estimates of the temperature, deformation resistance and rolling load of the rolled material for each pass by using the rolling reduction Ah (or the thickness h.) and the temperature T and hardness Q of the rolled material inputed to the first arithmetic unit 6, and calculates according to the Hookes law the screw-down position S; for each pass at which the rolling mill should be set. The screw-down position S, is transmitted to the gate circuit 10 after completion of the (:'l )th passing.

The gate circuit 10 receives ON-OFF signals from the load cell 9 and transmits an output signal to the screwdown position setting means 1] indicating the screwdown position set value S, for the next following passing.

The screw-down position setting means 11 actuates the screw-down electric motor 3 in order to effect screw-down positioning by setting the roll pass of the rolling mill 2 at a desired degree of opening. Upon completion of positioning, the material I is fed to the rolling mill 2 to effect an ith passing through the roll pass.

A modification of the invention will now be described. FIG. 6 shows another method by which the rolling reduction Ah, for each pass is calculated by the second arithmetic unit 7. In the modification shown in FIG. 6, the following relation is used:

Ah, a .Ah,,. (24) where the coefficient a, is a function of the pass number i and obtained by the following equation:

In equation (25), a is expressed in a cubic of the ratio of the pass number i to the total number n of passes, which can be solved empirically. The coefficients d, e, fand g in equation (25) should satisfy the following conditions:

1. Limitations are placed on the rolling reduction by taking temperature control into consideration in passes in initial stages;

2. The value of rolling reduction in passes in intermediate stages is below that of the rolling reduction limit value Ah max;

3. Limitations are placed on the rolling reduction by taking contour control into consideration in terminating stages; and

By using the coefficients a, e, fand g which satisfy these conditions, the distribution ratio a,- for each pass is calculated from equation (25 and the rolling reduction Ah,- for each pass is determined from equation (24). The screw-down position is set by utilizing the rolling reduction h,- obtained in this way, and the screwdown position is set in the same manner as aforemen tioned to carry out rolling.

[t is to be understood that the invention is not limited to the embodiment described above and that the method according to the invention can be carried worked at high speed by means of a simple mechanism by utilizing a computer.

From the foregoing description, it will be appreciated that the rolling method provided by the present invention is suitable for effecting temperature control and contour control satisfactorily, because the values for rolling reductions are selected such that the value of rolling reduction for each pass in initial stages of the rolling operation is smaller than that of the mean rolling reduction, and the value of rolling reduction for each pass in terminating stages is also smaller. This enables to produce rolled products which are high in quality and stable.

In the above-mentioned embodiments, the mean rolling reduction is obtained by using the smallest value of the maximum limit rolling reduction Ah,, the load limited rolling reduction Ah,,, and the torque limited rolling reduction Ahr. However, in some cases the mean rolling reduction may be obtained by using one of the limited rolling reductions, or the mean value of the limited rolling reductions.

I claim:

I. A rolling method for rolling mills comprising the steps of:

obtaining a mean rolling reduction Ah and the number n of passes for carrying out rolling in a minimum period of time from the rolling specifications and by detecting the temperature and thickness of a material to be rolled at the entrance side of the rolling mill, and

determining the rolling schedule, such that the value of rolling reduction selected for each pass in initial and terminating stages of the rolling operation is smaller than that of the mean rolling reduction and yet the total rolling reduction is equal to the product of the mean rolling reduction Ah and the number n of passes.

2. A rolling method as claimed in claim 1, wherein said mean rolling reduction is calculated by using a value which is obtained by multiplying the smallest value of a maximum limit rolling reduction (Ah a load limited rolling reduction (Ah,,) and a torque lim- 12 ited rolling reduction (AM) by a coefficient d1 (0 4:

3. A rolling method as claimed in claim 1, wherein the ratio of the total rolling reduction to a value obtained by multiplying a load limited rolling reduction by a coefficient less than I, is used as the number of passes by counting as a whole number the fraction of the value of the ratio obtained.

4. A rolling method as claimed in claim 1, wherein the ratio of the total rolling reduction to a value obtained by multiplying a torque limited rolling reduction by a coefficient less than I, is used as the number of passes by counting as a whole number the fraction of the value of the ratio obtained.

5. A rolling method as claimed in claim 1, wherein the ratio of the total rolling reduction to a value obtained by multiplying the smallest value of a maximum limit rolling reduction (A11 a load limited rolling reduction (M1,) and a torque limited rolling reduction (AM) by a coefficient less than l, is used as the number of passes by counting as a whole number the fraction of the value of the ratio obtained.

6. A rolling method as claimed in claim I, wherein the ratio of the total rolling reduction to a value obtained by multiplying the mean value of a maximum limit rolling reduction (Ah a load limited rolling reduction (Ah,,) and a torque limited rolling reduction (Ahr) by a coefficient smaller than 1, is used as the number of passes by counting as a whole number the fraction of the value of the ratio obtained.

7. A rolling method as claimed in claim I, wherein the rolling reduction for each pass in the initial and terminating stages is obtained by multiplying the mean rolling reduction by a distribution ratio.

8. A rolling method as claimed in claim I, wherein the rolling reduction for each pass in the initial and terminating stages is obtained from the thickness of a parent material, the thickness of a product and a cumulative distribution ratio.

9. A rolling method as claimed in claim 3, wherein said load limited rolling reduction is obtained from the detected values of the temperature and thickness of the material to be rolled.

10. A rolling method as claimed in claim 4, wherein said torque limited rolling reduction is obtained from the detected values of the temperature and thickness of the material to be rolled.

II. A rolling method as claimed in claim 7, wherein said distribution ratio is obtained as a function of the number of passes.

12. A rolling method as claimed in claim 8, wherein said cumulative distribution ratio is obtained as a func- 

1. A rolling method for rolling mills comprising the steps of: obtaining a mean rolling reduction Delta h and the number n of passes for carrying out rolling in a minimum period of time from the rolling specifications and by detecting the temperature and thickness of a material to be rolled at the entrance side of the rolling mill, and determining the rolling schedule, such that the value of rolling reduction selected for each pass in initial and terminating stages of the rolling operation is smaller than that of the mean rolling reduction and yet the total rolling reduction is equal to the product of the mean rolling reduction Delta h and the number n of passes.
 2. A rolling method as claimed in claim 1, wherein said mean rolling reduction is calculated by using a value which is obtained by multiplying the smallest value of a maximum limit rolling reduction ( Delta hx), a load limited rolling reduction ( Delta hp) and a torque limited rolling reduction ( Delta h Tau ) by a coefficient phi (0 < phi < or = 1).
 3. A rolling method as claimed in claim 1, wherein the ratio of the total rolling reduction to a value obtained by multiplying a load limited rolling reduction by a coefficient less than 1, is used as the number of passes by counting as a whole number the fraction of the value of the ratio obtained.
 4. A rolling method as claimed in claim 1, wherein the ratio of the total rolling reduction to a value obtained by multiplying a torque limited rolling reduction by a coefficient less than 1, is used as the number of passes by counting as a whole number the fraction of the value of the ratio obtained.
 5. A rolling method as claimed in claim 1, wherein the ratio of the total rolling reduction to a value obtained by multiplying the smallest value of a maximum limit rolling reduction ( Delta hx), a load limited rolling reduction ( Delta hp) and a torque limited rolling reduction ( Delta h Tau ) by a coefficient less than 1, is used as the number of passes by counting as a whole number the fraction of the value of the ratio obtained.
 6. A rolling method as claimed in claim 1, wheRein the ratio of the total rolling reduction to a value obtained by multiplying the mean value of a maximum limit rolling reduction ( Delta hx), a load limited rolling reduction ( Delta hp) and a torque limited rolling reduction ( Delta h Tau ) by a coefficient smaller than 1, is used as the number of passes by counting as a whole number the fraction of the value of the ratio obtained.
 7. A rolling method as claimed in claim 1, wherein the rolling reduction for each pass in the initial and terminating stages is obtained by multiplying the mean rolling reduction by a distribution ratio.
 8. A rolling method as claimed in claim 1, wherein the rolling reduction for each pass in the initial and terminating stages is obtained from the thickness of a parent material, the thickness of a product and a cumulative distribution ratio.
 9. A rolling method as claimed in claim 3, wherein said load limited rolling reduction is obtained from the detected values of the temperature and thickness of the material to be rolled.
 10. A rolling method as claimed in claim 4, wherein said torque limited rolling reduction is obtained from the detected values of the temperature and thickness of the material to be rolled.
 11. A rolling method as claimed in claim 7, wherein said distribution ratio is obtained as a function of the number of passes.
 12. A rolling method as claimed in claim 8, wherein said cumulative distribution ratio is obtained as a function of the number of passes. 